Question: The grades on a chemistry midterm at Almond are normally distributed with $\mu = 71$ and $\sigma = 4.5$. Michael earned a $74$ on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Michael's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{74 - {71}}{{4.5}}} $ ${ z \approx 0.67}$ The z-score is $0.67$. In other words, Michael's score was $0.67$ standard deviations above the mean.